|
%I #11 Mar 10 2023 12:39:55
%S 1,1,1,3,5,11,17,29,41,61,81,111,141,183,225,281,337,409,481,571,661,
%T 771,881,1013,1145,1301,1457,1639,1821,2031,2241,2481,2721,2993,3265,
%U 3571,3877,4219,4561,4941,5321,5741,6161,6623,7085,7591,8097,8649,9201,9801,10401
%N Number of 1423-avoiding even Grassmannian permutations of size n.
%C A permutation is said to be Grassmannian if it has at most one descent. A permutation is even if it has an even number of inversions.
%C Avoiding any of the patterns 2314 or 3412 gives the same sequence.
%H Juan B. Gil and Jessica A. Tomasko, <a href="https://arxiv.org/abs/2207.12617">Pattern-avoiding even and odd Grassmannian permutations</a>, arXiv:2207.12617 [math.CO], 2022.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F G.f.: -(x^5-x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
%F a(n) = 1 - 5*n/24 + n^3/12 - (-1)^n * n/8. - _Robert Israel_, Mar 10 2023
%e For n=4 the a(4) = 5 permutations are 1234, 1342, 2314, 3124, 3412.
%p seq(1 - 5*n/24 + n^3/12 - (-1)^n * n/8, n = 0 .. 100); # _Robert Israel_, Mar 10 2023
%Y Cf. A356185, A361272, A361273, A361274.
%Y For the corresponding odd permutations, cf. A005993.
%K nonn,easy
%O 0,4
%A _Juan B. Gil_, Mar 10 2023
|
